In known magnetic resonance imaging (MRI), image data is commonly acquired by raster scanning a spatial Fourier transform domain called k-space, thereby sampling k-space lines, and taking an inverse Fourier transform of the samples. MR imaging is limited by the time required to trace the k-space scan lines. However, accelerating MRI by reducing the number of k-space lines acquired is accompanied by reductions in image quality; accelerated parallel RF coil MRI undersamples k-space, using fewer lines spaced farther apart, reducing the field of view (FOV). This introduces aliasing when the object is larger than the reduced FOV, however the use of parallel RF coil imaging and parallel receivers resolves this aliasing and produces a full-FOV image from accelerated acquisitions.
Compressed sensing (CS) uses the compressibility of MR images to reconstruct images from randomly undersampled data. Methods like SENSE (SENSitivity Encoding), GRAPPA (Generalized autocalibrating partially parallel acquisitions), and SPIRiT (Compressed Sensing Parallel Imaging MRI) also are effective for reconstructing images from undersampled data, but these methods are affected by noise amplification or residual aliasing at high levels of acceleration. The combination of SENSE or SPIRiT with CS addresses the shortcomings of accelerated parallel imaging and achieves acceleration beyond what is achievable with either approach individually. The combination of GRAPPA with a sparsity model is more complicated due to characteristics of GRAPPA including the presence of a calibration step, the use of uniformly-spaced (nonrandom) undersampling, and the reconstruction of multiple channel images rather than a single combined image. A system according to invention principles addresses these deficiencies and related problems.